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Heterogeneous Reaction Engineering: Theory and Case Studies

Heterogeneous Reaction Engineering: Theory and Case Studies. Module 4 Analysis of Local Transport Effects in Gas-Liquid-Solid Systems. P.A. Ramachandran rama@wustl.edu. Outline. Transport Effects Diagnostic plots for slurry systems Partial wetting and implications

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Heterogeneous Reaction Engineering: Theory and Case Studies

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  1. Heterogeneous Reaction Engineering: Theory and Case Studies Module 4 Analysis of Local Transport Effects in Gas-Liquid-Solid Systems P.A. Ramachandran rama@wustl.edu

  2. Outline • Transport Effects • Diagnostic plots for slurry systems • Partial wetting and implications • Slurries containing fine particles

  3. ci Ni catalyst Ni ci Vapor film Bulk vapor Liquid film Bulk liquid T E E Liquid film T Heterogeneous Liquid-Phase Reaction Phenomena Challenges: 1. Identifying reaction(s) and their location(s) 2. Accounting for internal and external catalyst wetting / holdup phenomena

  4. Mass Transfer Resistances in Gas-Liquid-Solid Systems

  5. Local Rate of Reaction for Gas-Liquid-Solid Catalyzed Systems A (g) + b B (l) P (l) Gas-Liquid Mass Transfer: RA = kLaB (A* - AL ) Liquid-Solid Mass Transfer for A: RA = ksap (AL - As ) Liquid-Solid Mass Transfer for B: RB = ksap (BL - Bs ) Intra particle Diffusion with Reaction: RA = wc(As, Bs)kmnAsmBsn

  6. Intraparticle Diffusion Limitations • Solution of the reaction-diffusion equations in the catalyst particle for some simple reactions results in effectiveness factor-Thiele modulus relationship similar to that represented by the enhancement factor-Hatta number relationship for gas-liquid reactions Other details: Froment & Bischoff (1979)

  7. Observed Rate - 1st Order Reaction in a Gas-Liquid-Solid System • For linear kinetics and the slow reaction regime, an overall resistance can • be defined that includes the gas-liquid and liquid-solid mass transfer • and reaction terms, including intraparticle diffusion limitations -1 w

  8. A*/RA A*/RA 1/w 1/w A*/RA 1/w Diagnostic Plots: First Order Case Gas-Liquid Mass Transfer Controls the Process Negligible Gas-Liquid Resistance Slope = rcr Intercept = rb Intermediate Case

  9. A*/RA 1/w Diagnostic Plots (contd) A*/RA Increasing resistance to gas absorption Decreasing Particle Size 1/w m > 1 m = 1 m < 1 m = 0 A*/RA 1/w Schematic Plots for other Higher Orders

  10. Commonly-Used Kinetic Models for Gas-Liquid-Solid Systems A (g) + b B (liq) P (liq) Mechanism Rate Form 1. Single site adsorption of dissolved gas 2. Dissociative adsorption of dissolved gas 3. Adsorption of both A & B on single sites 4. General single site adsorption for N species

  11. Overall Effectiveness Factorfor a (m,n) order Reaction = f(sA , fo) (1) where: (2) (3)

  12. Overall Effectiveness Factorfor a Single-Site L-H Rate Form Example: Glucose Hydrogenation Ramachandran & Chaudhari, 1983

  13. Analysis of External Mass Transport Resistance • Overall mass transfer of H2 (gas) to catalyst surface is : Rgas = MA(A*-As), A* - gas concentration in the liquid phase (using Henry’s Constant) • Gas consumption by all reactions: • Considering As = 0 , we have If LHS > > RHS, then no mass transfer resistance !

  14. Analysis of Internal Resistance (within the Catalyst Pellet) n = reaction order, taken as unity robs = net rate of consumption of limiting Reactant (initial rate) Cb = concentration of limiting reactant in liquid Deff = effective diffusivity = DABp/τ p= particle porosity ~ 0.5 τ = totuosity = 2 DAB = binary diffusivity (Wilke Chang correlation L = (characteristic length) Vp/Sp • Weisz-Prater criterion is used Internal Resistance is considered negligible if We0.5 < 0.2

  15. Parameter Estimation Method • Step-by-step approach • Start with a temperature data set • Identify the reactions • Identify the reaction form (reaction rate): Where, Aoj and Ej are estimated !

  16. Kinetic Parameter Estimation (contd.) • Non-linear Optimization Problem • Identify and select the for the objective function • Identify the species adsorbed, if any (C1 to C5 here, as an example) • Develop parameter estimation program and the autoclave model / Slurry reactor model • Autoclave model predicts the species concentration at every instant (for the operating conditions) – set of differential equations can be solved by VODE routine from NETLIB libraries • Levenberg-Marquardt algorithm for parameter estimation – UNLSF routine from IMSL libraries

  17. Trickle-Bed Reactors

  18. Fixed-Bed Multiphase Reactors (a) Trickle - Bed (b) Trickle - Bed (c) Packed - Bubble Flow Cocurrent Countercurrent Cocurrent downflow flow upflow Semi-Batch or Continuous Operation; Inert or Catalytic Solid Packing

  19. Plug-flow high conversion Low liquid holdup less homogeneous reactions High specific reaction rate Temperature control possible by liquid vaporization High pressure operation possible Minimal catalyst handling issues Process flexibility, reasonable throughput limitations Lower capital & operating costs Intraparticle diffusion resistance Incomplete contacting/wetting High pressure drop Temperature control problems hot spots Scale-up and design is complex Attrition and crush resistant catalyst is required Dirty process streams cannot be used plugged or fouled bed Catalyst loading is complicated Trickle-Bed Reactors - Pros and Cons - Pros Cons

  20. Axial & radial RTD’s Flow regime Pressure drop Liquid holdup Liquid flashing Interphase transport Liquid distribution Heat transfer Energy dissipation LocaL texture of liquid flow (films, rivulets, stagnant pockets) Local irrigation and wetting Liquid holdup in pores Local transport between gas and flowing and stagnant liquid, and solid Local transport between flowing liquid, stagnant liquid, and solid Local transport between gas and vapor-filled pores Fundamental Phenomena in Trickle Bed Reactors Macroscale Microscale

  21. Classification of TBR Processes Based on Volatility 1. Nonvolatile liquid reactant • Rate limiting reactant - Liquid - Gas - Both 2. Volatile liquid reactant • Rate limiting reactant - Liquid - Gas - Both Reaction occurs only on wetted catalyst Reaction occurs both on wet and dry catalyst

  22. Key TBR Design Parameters • Flow regime • Pressure drop • Liquid holdup • Liquid - solid contacting • Interphase transport coefficients • Intraparticle diffusion • Extent of liquid volatilization • Reaction kinetics • Thermo - physical constants

  23. Flow Regime Structures for Gas-Liquid Flow in Fixed-Beds Trickle-Flow Pulse-Flow Spray-Flow Bubble-Flow Mewes, Loser, and Millies (1999)

  24. Three Key Factors Affecting Flow Regimes 1. Throughput of gas and liquid L - liquid mass velocity G - gas mass velocity L / G - ratio of mass velocities 2. Physical properties of the gas and liquid - viscosity - surface tension - density 3. Foaming or non-foaming characteristics of the liquid

  25. Factors Affecting Choice of L / G • Stoichiometry of the reaction • Pressure drop limitations • Establishment of desired flow regime • Foaming characteristics of liquid • Heat removal requirement • Maximum allowed Tad

  26. Flow Regime Map for Gas-Liquid Flow in Fixed-Beds Gianetto, Baldi, Specchia and Sicardi, AIChEJ (1978)

  27. Effect of Bed Prewetting and Hysteresis Effects CCD Video Imagesof Liquid Flow in 2-D Beds channel flow film flow L= 3.52 Kg/m2.s

  28. Models for Trickling to Pulsing Flow Regime Transition • Macroscopic model - balance of inertial and capillary forces • Grosser, Carbonell & Sundaresan, AIChE J (1988) • Attou & Ferschneider, CES (1999) • Microscopic model - pore blockage by balance of inertial and capillary forces • Ka Ng, AIChE Jnl (1986) • Microscopic model - wave formation on surface of liquid film • Holub, Dudukovic & Ramachandran, AIChE J (1993)

  29. Estimation of Pressure Drop for Two-phase Flow in Packed-Beds Various empirical correlations based on: • Lockhart -Martinelli parameter • Two - phase friction factor • Energy dissipation parameter • Relative permeability parameter • Other dimensionless parameters

  30. Key Pressure Drop Equation Parameters • Single - phase pressure drop • Lockhart -Martinelli parameter • Two - phase friction factor Validity: • Low and high Interaction regimes • Non-foaming and foaming systems

  31. Pressure Drop - Summary • Correlations based on single-phase gas and liquid DP (Ergun equation) • Lockhart-Martinelli (1949), Larkins et al. (1961), Specchia & Baldi (1974) - separate for low and high interaction, Kan & Greenfield (1978) - hysteresis effect on DP • Flow models • Relative permeability model: Saez & Carbonell, AIChE J (1985); Levec, Saez & Carbonell, AIChE J (1985); Saez, Levec & Carbonell, AIChE J (1985) • Slit model: Holub, Dudukovic & Ramachandran, CES (1992); AIChE J (1993); Al-Dahhan, Khadilkar, Wu, & Dudukovic IEC Res. (1998); Iliuta & Larachi, CES (1999) • Fluid- fluid interface model: Attou, Boyer & Ferschneider, CES (1999), Attou & Ferschneider, CES (1999)

  32. Liquid Holdup - Key Definitions • Liquid holdup(HL , L ) is the fraction of reactor volume that is occupied by liquid (m3 liquid / m3 reactor). L = VL / VR • Liquid saturation(L , L ) is the fraction of external bed voidage (B ) occupied by liquid (m3 liquid / m3 voids). L = L / B • Fractional pore fill-up(Fi) is the fraction of catalyst pore volume occupied by liquid (m3 liquid / m3 pore volume).

  33. Key Liquid Holdup Relationships Total Bed Voidage= External Voidage + Internal Voidage t = B + p ( 1 - B ) Total Liquid Holdup= External Holdup + Internal Holdup L = LE + L Internal Holdupfor Liquid-Filled Catalyst Pores (Fi = 1) LI = F i p ( 1 - B ) External Liquid Holdup= Dynamic Holdup + Static Holdup LE = LD + LS

  34. Typical External Holdup Values External Liquid Holdup= Dynamic Holdup + Static Holdup LE = LD + LS 0.1 < LE < 0.25 ( or higher at high L / G )

  35. Liquid Holdup - Summary Contributions to the overall liquid holdup • Internal liquid holdup (inside particle) ~ equal to particle porosity • External liquid holdup • dynamic (flowing liquid) - depends on flow regime and is determined by viscous, gravity and inertial forces • static - volume fraction of liquid retained when a pre-wetted bed is drained, from balance of gravity and surface tension forces HL= HLD + HLSe+ HLi = HLD + HLSe+ ip(1- B) HL, HLD & HLe correlations for low & high interaction regime • Separate correlations for low and high interaction regimes • Empirical: Larachi et al. (1991), Lara-Marquez et al. (1992) • Phenomenological: Holub et al. (1992, 1993); Al-Dahhan & Dudukovic (1994)

  36. Pressure Drop and Liquid Holdup Correlations MARE (%)* eLDP / L Iliuta & Larachi (1999) 18 27 Ellman et al. (1988, 1990) 23 54 Saez et al. (1985) 22 41 Al-Dahhan & Dudukovic (‘95, ‘96) 17 32 Larachi et al. (1991) 22 73 *Mean Absolute Relative Error Carbonell, O&G Sci & Tech, vol 55 (4) (2000)

  37. Key Transport Resistances • Gaseous reactant resistances 1 - Gas-to-liquid resistance 2 - Liquid-to-solid resistance 3 - Intraparticle diffusion and kinetic resistances • Liquid reactant resistances 1 - Liquid-to-solid resistance 2 - Intraparticle diffusion and kinetic resistances • Heat transfer resistances 1 - Bulk gas-to-particle 2 - Bulk liquid-to-particle 3 - Intraparticle

  38. Transport Parameter Correlations kLaB - Gas to liquid ( liquid - side ) volumetric mass transfer coefficient kSL - Liquid to actively wetted solid mass transfer coefficient kSg - Gas to dry solid mass transfer coefficient h - Overall heat transfer coefficient e - Effective conductivity of particles

  39. Interphase Mass Transfer Correlations - Summary Liquid side of gas-to-liquid mass transfer • Separate correlations for low and high interaction regimes • Wild et al. (1992); Larachi (1991); Cassanello et al. (1996) Gas side of gas-to-liquid mass transfer • For most situations negligible resistance • Gotto et al. (1977); Fukushima & Kusaka (1978) Liquid-to-solid mass transfer • Some have separate correlations for low and high interaction regimes • Goto & Smith (1975), Satterfield et al. (1978), Specchia et al. (1978)

  40. Liquid - Solid Contacting in TBR’s • Incomplete liquid - solid contacting can occur due to: 1. Reactor- scale (gross liquid maldistribution) 2. Particle - scale (local catalyst incomplete wetting) • Internal particle incomplete contacting is unlikely in the absence of highly exothermic reactions • External particle incomplete contacting is likely in the trickle - flow regime when Lm < 5 kg / m2 - s

  41. External Contacting EfficiencyLow Gas-Liquid Interaction Regime where: D = Dynamic liquid saturation

  42. Liquid-Solid Contacting - Summary Combining flow pattern deviations from ideal liquid plug flow, and incomplete catalyst wetting: • Liquid not in plug flow and there is no radial mixing, but all catalyst is wetted • Liquid not in plug flow and extensive radial mixing, and all catalyst is wetted • Partial external wetting of catalyst • Partialinternal wetting of catalyst Correlations for liquid-solid contacting: • Ruecker & Agkerman (1987), Ring & Missen (1991), Al-Dahhan & Dudukovic (1995)

  43. Intraparticle Diffusion Resistance Conventional Thiele-modulus/effectiveness factor approach needs to be modified to account for partial external and intraparticle wetting: • Mills & Dudukovic (1980) solved the diffusion-reaction equations for partial external wetting for slab, cylinder and sphere-shaped particles • The numerical solution can be approximated by weighted average of effectiveness factor of totally wetted and totally dry particles, the weighting factor being the contacting efficiency TB = CE W + (1- CE) NW • Internal wetting effects have been largely ignored

  44. Catalyst Effectiveness Factor for a Differential TBR • Assume: (1) Gas-limiting or volatile liquid-limiting reactant (2) First-order reaction (3) Incomplete external wetting, complete internal wetting • Approximate solution only possible for large modulus p

  45. Overall Effectiveness Factor for a Trickle-Bed Reactor (limiting reactant in Gas phase), hO CE = external liquid-solid contacting efficiency CE < 1 for cocurrent downflow; CE = 1 for upflow Increasing ηCE decreases conversion ! LHSV based scale-up alone is not suitable !

  46. Overall Effectiveness Factor for a Trickle-Bed Reactor, (limiting reactant in liquid phase) hO Increasing ηCE increases conversion ! LHSV based scale-up is suitable !

  47. Trickle-Bed ReactorCatalyst Effectiveness FactorsOverall effectiveness factor, hO • Both external and internal transport resistances are included

  48. Comparison of Effectiveness Factors Calculated From Previous approximate Solution and Actual Numerical Simulation

  49. Rigorous Multicomponent Diffusion Modeling- Gas Liquid Interphase Function Vector - Khadilkar et al., 1998 CREL

  50. General Geometry • Discuss MFS use here • See muthana. Eusebio paper

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